Yeh, "if you ain't peeing, you ain't drinking enough water. However, "water" can also be had in the food you eat. Some animals get all or nearly all of their water from their food. We can't do that, but every little bit helps. Which is the whole point of this recycling thingie. More water input to the soldier for the same logistics burden, or in cases where troops temporarily have no access to resupply of water.
Because of perspiration, the system isn't closed, and water must still be supplied of course. But not as much. Might make the available supplies of water stretch just far enough so that no one dies of dehydration.
Actually it's not even quite that simple. Humans, and other animals, also make water just in living. Basically we burn carbohydrates, fats and protein, to make water, carbon dioxide and various other gases in much smaller amounts, along with the energy that is (part of) the point of the exercise.
The combusted water is exhaled.